An oligarch is one of the select few people who rule or influence leaders in an oligarchy—a government in which power is held by a select few individuals or a small class of powerful people.
Oligarchs can be the actual leaders, or they can influence or control the decisions that the leaders make (meaning they’re the ones “pulling the strings” behind the scenes).
Oligarchy is never used as an official term for a form of government (like monarchy is, for example)—it’s almost always applied as a criticism of such situations. It is frequently used as a way of pointing out the influence of the wealthy and powerful in politics and government—an influence that’s typically used to benefit themselves.
What's your point?